GATE CS 2014 Q9: Function Properties on Sets (Images & Preimages)

Computer Sciences > GATE 2014 SET-3 > Functions

Let X and Y be finite sets and f: X → Y be a function. Which one of the following statements is TRUE?

For any subsets A and B of X, |f(A ∪ B)| = |f(A)| + |f(B)|

For any subsets A and B of X, f(A ∩ B) = f(A) ∩ f(B)

For any subsets A and B of X, |f(A ∩ B)| = min{|f(A)|, |f(B)|}

For any subsets S and T of Y, f⁻¹(S ∩ T) = f⁻¹(S) ∩ f⁻¹(T)

Correct : d

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